Deuteronomy Chapter 25

You shall remember what [Amalek] did to you: [The juxtaposition of these passages teaches us that] if you use fraudulent measures and weights, you should be worried about provocation from the enemy, as it is said: “Deceitful scales are an abomination of the Lord” (Prov. 11:1), after which the [next] verse continues,“When willful wickedness comes, then comes disgrace.” [That is, after you intentionally sin by using deceitful scales, the enemy will come to provoke you into war, and this will be a disgraceful matter to you]. — [Tanchuma 8]

how he happened upon you on the way: Heb. קָרְךָ, an expression denoting a chance occurrence (מִקְרֶה). - [Sifrei 25:167] Alternatively, an expression denoting seminal emission (קֶרִי) and defilement, because Amalek defiled the Jews by [committing] homosexual acts [with them]. — [Tanchuma 9] Yet another explanation: an expression denoting heat and cold (קוֹר). He cooled you off and made you [appear] tepid, after you were boiling hot, for the nations were afraid to fight with you, [just as people are afraid to touch something boiling hot]. But this one, [i.e., Amalek] came forward and started and showed the way to others. This can be compared to a bathtub of boiling water into which no living creature could descend. Along came an irresponsible man and jumped headlong into it! Although he scalded himself, he [succeeded to] make others think that it was cooler [than it really was]. — [Tanchuma 9]

and cut off: [The word וַיְזַנֵּב is derived from the word זָנָב, meaning “tail.” Thus, the verse means: Amalek] “cut off the tail.” This refers to the fact that Amalek cut off the members [of the male Jews,] where they had been circumcised, and cast them up [provocatively] towards Heaven [exclaiming to God: “You see! What good has Your commandment of circumcision done for them?”]- [Tanchuma 9]

ויזנב בך: מכת זנב, חותך מילות וזורק כלפי מעלה:

all the stragglers at your rear: Those who lacked strength on account of their transgression. [And because these Jews had sinned,] the cloud [of glory] had expelled them [thereby leaving them vulnerable to Amalek’s further attack]. - [Tanchuma 10]

כל הנחשלים אחריך: חסרי כח מחמת חטאם, שהיה הענן פולטן:

you were faint and weary: faint from thirst, as it is written, “The people thirsted there for water” (Exod. 17:3), and [immediately] afterwards it says,“Amalek came [and fought with Israel]” (verse 17:8). - [Tanchuma 10]

He did not fear [God]: i.e., Amalek did not fear God [so as to refrain] from doing you harm. — [Sifrei 25:167]

ולא ירא: עמלק, אלהים, מלהרע לך:

19[Therefore,] it will be, when the Lord your God grants you respite from all your enemies around [you] in the land which the Lord, your God, gives to you as an inheritance to possess, that you shall obliterate the remembrance of Amalek from beneath the heavens. You shall not forget!

you shall obliterate the remembrance of Amalek: Both man and woman, infant and suckling, ox and sheep [camel and donkey] (God’s command to King Saul: see I Sam. 15:3), so that the name of Amalek should never again be mentioned (נִזְכָּר), from the word (זֵכֶר) , even regarding an animal, to say:“This animal was from Amalek.” - [Midrash Lekach Tov]